Factor analysis is a statistical data reduction technique used to explain variability among observed random variables in terms of fewer unobserved random variables called factors. It is useful to reduce the number of variables, by combining two or more variables into a single factor, thus “simplifying” the original dataset.

Factor analysis (FA) is especially useful in geochemistry when one has a known target or some other way to understand the meaning of the obtained associations. When failing this, the geologist is usually forced to “plot and see”, and then to select the FA that he believes is the most useful for the studied area.

I processed both the initial dataset and the three transformed versions using SYSTAT SSPS 10.0 for Windows, but you can use any other statistical program capable of factor analysis.

The fact that we have so many components as the result of the P.C.A., is an indication that we will not get good results this time. Equations 30 through 34 show the obtained factors.

Equation 30. FA8 for the IRL transformed dataset.

Equation 31. FA9 for the IRL transformed dataset.

Equation 32. FA10 for the IRL transformed dataset.

Equation 33. FA11 for the IRL transformed dataset.

Figures 47 through 50 shows the spatial distribution of these factors with respect to the location of our ore body.

§Conclusions and Recommendations on the Use of FA for the Transformed DatasetsEdit

As I mentioned earlier, for FA to be most useful, one needs to have a known target to calibrate it. The factor analysis applied to the CLR transformed data gave us three factors, but only one (FA5) was useful for targeting the ore body.

The factor analysis of the ALR transformed data (Factor 7) was good in general, but the best factors were obtained from the ILR transformed data, specially Factor 9 that not only gave the exact location of the ore body, but also its internal structure. Another efficient factor was FA11, but it definitively required calibration based on a known target.

So answering the question from page 41, yes, the factor analysis of the IRL transformed data will be more effective than the factor analysis of the raw data as a tool for locating the ore deposit.